Shortcomings of Existing CA Models

Despite the inherent simplicity and its supremacy in simulation expedition, one might find that most existing CA models dealt with pure traffic (only one type of vehicle such as cars) on freeways. Incorporation of more realistic CA rules into the simulation of mixed traffic (various types of vehicles such as cars, motorcycles, buses) on urban streets or surface roads are comparatively much less addressed. It is most likely that this bias mainly suffers from the restraint circumvented by the coarse cell systems utilized by existing CA models.

Figure 3-1. Erratic motorcyclists’ behaviors in congested urban traffic, such as sneaking into traffic jam and transverse crossing between two adjacent still vehicles.

As mentioned, most existing CA models utilized comparatively coarse cell system proposed in the primitive NaSch model (refer to Figure 2-3) in which each lane only allowed to be occupied by a single vehicle laterally. One crucial defect aroused from such coarse cell system is that it would be difficult to implement mixed traffic simulations where vehicles have different sizes (length and width) and/or possess distinct behavior. For example, it is

ubiquitous in many Asian urban streets that motorcycles oftentimes move concurrently with the cars by sharing the “same lane” (see Figure 3-1).

According to Figure 3-1, one may find that some erratic motorcyclists do not even follow the lane disciplines at all. They may make lateral drifts breaking into two moving cars. Once blocked by the front vehicles, they even make wide transverse crossings through the gap between two stationary cars in the same lane, in order to keep moving forward. In this circumstance, obviously, conventional coarse cell system is deficient to describe various vehicle sizes with their coupled interactions. However, though the mixed traffic contexts hitherto are seldom studied through CA modeling, an in-depth understanding of mixed traffic behaviors can be imperatively important in many Asian cities where motorcycles are prevailing.

Another shortcoming of the coarse cell system is the derived low resolution which stands as the crucial barrier for implementing CA models into urban traffic simulation. In urban streets, the speed limits are usually low. For instance, if the speed limit is 60kph, there would be only three speed options available for any vehicle—0, 28kph and 56kph provided that the cell system in NaSch model (7.5m) is used for CA simulation. This is apparently not so practical if one wishes to scrutinize in detail the microscopic traffic features or to trace the realistic behavior of an individual vehicle. Furthermore, most existing CA works only considered basic heterogeneity among vehicles, including various speed limits and/or different vehicle lengths. For instance, Chowdhury et al (1997), Nagel et al (1998), Ebersbach et al (2000) and Wang et al (2007) analyzed the impact of partial vehicles equipped with lower or higher maximum speed in the traffic flow. Ez-Zahraouy et al (2004) evaluated the effect of mixture lengths of vehicles on the traffic flow in a single-lane context. In Knospe’s et al (2000) paper, a two-lane system with smaller cell sizes and different types of vehicles were studied. Kerner et al (2004) further evaluated both the effects of different vehicle lengths and various maximum speeds. In these CA models, except that by Knospe et al (2000), Wang et al (2007) and Kerner et al (2004), the small vehicles occupy one cell, while the big ones take two cells, but none ever take the impact of vehicular widths into consideration. The only existing effort taking vehicular width into account is perhaps that by Meng et al (2007). They tried to divide a single-lane into three sub-lanes and thus allowed the introduction of motorcycles into simulation.

As for urban traffic simulations, the existing CA studies in this regard can be categorized into two approaches. The first approach considers an abstract network which assumes a two-dimensional lattice and focuses on the investigation of phase transitions, e.g., Simon et al (1998), Chowdhury et al (1999) and Watanabe (2003). The second approach tries to describe the real-world traffic prevailing on the surface roadways in populated cities, e.g., Jiang et al (2006) and Spyropoulou (2007). Since these models basically followed the NaSch’s coarse cell system, inevitably the vehicular speeds had merely three theoretical options (0, 1, 2) to cope with the prevailing urban speed limits.

Moreover, for CA simulation there is one common defect yet rectified—abrupt deceleration when vehicles encounter stationary obstacles or traffic jams. In fact, deceleration limitation was seldom been considered in the past; perhaps suffered from the utilized coarse cell system. Most CA models just considered a collision-free criterion explicitly by imposing arbitrarily large deceleration rates, which can be far beyond the practical braking capability under prevailing pavement and tire conditions. Consequently, most previous CA simulations have revealed that, for sake of collision prevention, a vehicle can take as short as 1 second to come to a complete stop, even from a full speed (e.g., 100kph), apparently exceeding the vehicular deceleration capabilities.

Such unrealistic abrupt deceleration can be easily identified via checking the vehicular speed profiles in the front of traffic jams or stationary obstacles.

When scrutinizing the existing efforts, one may agree that simulation through CA model has led to satisfactory outcome if only long-term average traffic features are concerned or only macroscopic traffic phenomena or global traffic parameters are examined; because the effects of locally realistic deceleration have been smoothed out. However, if we want to scrutinize in detail the microscopic traffic parameters around signalized intersections or the neighborhood of some unexceptional scenarios, such as an accident vehicle or a work zone blocking the partial highway lanes, it is evident that the deceleration rule in CA model requires further revisions.

To overcome the above-mentioned impediments for implementing CA into urban traffic simulation, we will propose three major modifications that

differ from the traditional CA models. First we propose to establish a refined CA cell system. For this, the concept “cell”, “site”, “common unit” (short for CU hereinafter) and the relationships among them will be defined. Next, Daganzo’s (1997) two-dimensional generalized traffic variables—density k(A) and flow q(A)—are further extended to three-dimensional ones to account for the distinct vehicle widths and lane widths. As such, the generalized spatiotemporal occupancy ρ(S) and flow rates q(S) are defined. Finally, upon these two amendments, we further suggest the piecewise-linear variation of vehicular speed within each time-step. The methodology thereof is illustrated in detail in the following Sections.